I highly recommend buying some good guidebooks on Greece for starters. I used Lonely Planet and the Michelin Green Guide to plan our trip. I really believe that reading guidebooks is a more organized and helpful way to plan a trip. I use travel forums and the internet/blogs as secondary information, or for advice on restaurants, and to critique my itinerary AFTER I have read the guidebooks. My philosophy is that if someone can afford to travel to Europe, or anywhere else for that matter, they can afford to buy a guidebook or two. And I don't mean to be insulting when I say this.
I don't know where you heard you don't need to spend too much time in Athens and spend more time in Mykonos. I disagree with this advice. I have not been to Mykonos, but I do know that it has a party reputation. I am sure there are some nice areas on Mykonos, but it does seem to be primarily know for its partying and is very, very expensive.
I think you need a minimum of 4 nights in Athens, which is a very interesting city with so much history. The Acropolis and Parthenon, for starters, along with many other ancient ruins, awesome museums, the Plaka, Changing of the Guard, etc. If you go, be sure to visit the Athens Central Market with its fascinating meat and fish markets.
There are some people who will tell you not to visit Santorini because it's crowded, expensive and touristy. While it's all of that, it is also beautiful and unique with the villages overlooking the caldera, and with its white-washed buildings with blue dome roofs. Will you be willing to rent a car? We rented a car for a day while on Santorini and visited other parts of the island, such as the Akrotiri archaeological site, Akrotiri lighthouse, red sand beach, and black sand beach. It was one of our favorite days.
Another wonderful island is Naxos, which is quieter and more laidback than Santorini. We enjoyed staying at the edge of Agios Georgios Beach, within walking distance of Naxos Town. We rented a car for a day and visited several fishing villages and several mountain villages. Another awesome day!
How many nights do you have?
A possible itinerary could be Athens for 4 nights and Naxos or Santorini for 4 nights. Or you could consider Paros and Antiparos. I haven't been there but have read enough and seen enough photos that I am sure they would be awesome choices as well.
Or, if you don't want to visit an island, you could visit Nafplio on the Peloponnese Peninsula for 4 or 5 nights. Nafplio is a beautiful town located on the water and filled with bougainvillea. It's a lovely town to explore with a castle. And from Nafplio, you can visit such wonderful ancient ruins as Mystras, Epidaurus, Myceanae and many more.